Quantitative Reasoning – Find the number of Trout in the tank!

PSA 2014_XI_Q7. Trout are bred in a tank as fish for restaurants. Twenty trout are caught and each is tagged through the tail then released back into the tank. A week later, thirty trout are caught and it is found that two of them have a tail tag.

Based on this evidence alone, what estimate can be made of the total number of trout in the tank ?

1) 100
2) 300
3) 600
4) 1200

Ans: Out of thirty trouts randomly picked, two are found to be having the tail tag. Going by the probability (2/30), the next 30 trouts caught would have 2 with tags and so on. To accomodate 20 tagged trouts the total number of trouts in the tank could be 30*10 or 300. [Linear extrapolation]. Option 2.

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